Sentence examples for equations holding from inspiring English sources
Elementary algebra fixes some domain, typically the reals or complex numbers, and works with the equations holding within that domain.
The approximate symmetry reduction approach can be used to search for similar results of other perturbed nonlinear differential equations with small parameters, and it is worthwhile to summarize a general principle for the perturbed nonlinear differential equations holding analogous results.
These equations hold for any nonlinearity.
Thus making those equations hold guarantees optimality.
Similar equations hold for the higher order terms.
Thus, this means that the following equations hold: Set.
Hence, by, for sufficiently large, the following equations hold: (3.10).
The approximate field variables are selected such that all equilibrium equations hold in strong form.
Indeed, from (2.4) we deduce that the following equations hold: (3.14).
In particular, if P = Q, then above equations hold Q - a.e.
It is easy to check that the following equations hold (3.12).
